(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Hello again. First of all thanks to anyone who has replied to my previous questions.

Now, the question that troubles me is:

We are given a matrix A_{2x2}with some random values and we are asked to say if there is a linear map which has A as its map for the standar basis.

A= 2 1

-5 8

2. Relevant equations

3. The attempt at a solution

If A is the matrix of some linear map for the standar basis that means that:

f(1,0)=2(1,0) -5(0,1)

f(0,1)=1(1,0) +8(0,1)

so f(1,0)=(2,-5) and f(0,1)=(1,8)

Although the question only asks to say if such a linear map exists (it obviously does but i dont know how to prove it) I would be glad if someone could instruct me on finding formulas for linear maps when we have their matrix.

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# Homework Help: Finding the linear transformation of a matrix

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